In a driving system for a vehicle provided with a torque converter, a lock-up operation, whereat a power transmission is occurred without relying on a hydraulic pressure, causes a variation in a rotating movement of the engine to be directly transmitted to a gear train without any intervention of the torque converter. Dynamic dampers have thus been proposed, provided with planetary gear devices for obtaining an effective reduction of the rotating movement fluctuation during the execution of the lock-up operation. See Patent Documents 1 to 5. In any of dynamic dampers in these patent documents, a normal type of planetary gear device has been employed, which includes a plurality of planetary gears, each of which is formed as a straight pinion and has three rotating elements, that are a sun gear, a ring gear and a carrier, on which carrier the planetary gears are rotatably connected. The patent documents 1 to 5 are different with each other so long as the manners of mutual connection between the sun gears, the ring gears, the carriers and resilient members are concerned. These the documents 1 to 5 disclose however substantially identical ideas not only in the point of a structure that, among the sun gear, the ring gear and the carrier, a selected first element is connected to the crankshaft as a driving part and a selected second element is connected to the transmission device as a driven part, among the sun gear, the ring gear and the carrier, selected two elements are connected with each other by means of the resilient members for causing the selected two elements to participate a power transmission between the driving part and the driven part, on one hand and, on the other hand, among the sun gear, the ring gear and the carrier, a third element which is freely rotated and does not participate in the power transmission function makes the third element to operate as a damper mass but also in the point of the aimed function that an effective reduction of the fluctuation in the rotating movement is obtained by employing the planetary gear device.